Will Gluck’s “Annie,” which hits theaters on Dec. 19, transplants the beloved Depression-era musical into the present day by adding a pop spin on its classic tunes and a politically-tinged subplot about social media.

With that in mind, Cameron Diaz wanted to make sure Miss Hannigan felt contemporary, too. In previous incarnations of “Annie,” the villainess had been played as a booze-swilling spinster, but Diaz told The Huffington Post at a press event that she wanted to make her sexy and sassy -- and, above all,...